HCI 2022 Term 1 Revision Paper 1

1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Name: _________________________________ ( ) Class: _______ Date: __________ Revision Paper 1 Term 1 Topic s : Algebraic Manipulations/ Surds & Indices / Quadratic Express ions & Functions _______________________________________________________________________________________ • Answer all questions. • Omission of essential working will result in loss of marks. • The number of marks for each question or part question is shown in [ ]. • The use of calculators is allowed. _______________________________________________________________________________________ 1 The line x + y = 3 meets the curve x 2 – 2 x + 2 y 2 = 3 at two distinct points. Find the coordinates of these two points. [ 4 ] 2 Find the possible values of k for which the line 1−= kxy does not intersect the curve 32+= xy . [ 3 ] 3 Using a suitable substitution , solve the equation 14 16 66xx− += . [ 4 ] 4 S ketch the graph of 24 24 20y x x= − + , indicating clearly the coordinates of the turning point , x and y intercepts. [ 4 ] 5 Factorsie 4 3 232x x x−+ completely. [2] 6 The area of a rectangle ABCD is given by m 2 , and the length of side AB is m. Find , without using a calculator, the length of side B C in the form of m, where a and b are real numbers. [3] 7 Simplify into a single fraction 3 3 2 3 2 2 2 8 16 4 4 (4 2 ) x y xy x x y y x +− − −− . [3] ( )1 3 2+ ( )28+ ( 2)ab+

2 8 Given that 3 1 4 48 2 3 3 3 − +− + can be expressed in the form of 3ab+ , find the value of a and of b . [4] 9 Show that 24 12 10xx−+ is always positive for all real values of x . [3] 10 Show that the roots of 2 ( 2) 2x p x p+ − = are real. [3] 11 Solve the equation 25 50 2 12xx− − − = . [3] 12 In an experiment, the ends of a string of length 8 m are attached to two points A and B. A weight is fixed to point C on the string. The two parts of the string, AC and BC , are both straight. The length of BC is x m. (i) Given that AB = 7 m and angle ACB = 90o , form an equation in x and show that it reduces to 22 16 15 0xx− + = . [2] (ii) Given that AC is longer that BC, find the value of x. [2] 13 Find the solution set of each of the following inequalities: (i) 1832 + xx [2] (ii) 9)2( 2 +x [2]

3 14 The given diagram shows a quadratic curve with a y-intercept of 48 which crosses the x-axis at 4x=− and 6x= . (i) State the equation of the line of symmetry for the curve. [1] (ii) Find the equation of the parabola in the form 2 where 0y ax bx c a= + +  . [3] x y